Supersymmetry in noncommutative superspaces

TL;DR

This paper explores various deformations of noncommutative superspaces via Moyal-Weyl quantization, analyzing their supersymmetry properties and providing examples of deformed four-dimensional Lagrangians, including novel N>1 cases.

Contribution

It introduces new deformations of noncommutative superspaces, especially for extended supersymmetry, and examines their supersymmetry characteristics and resulting Lagrangians.

Findings

Different deformations correspond to constant background fields in string theory.

Supersymmetric and non-supersymmetric deformations are distinguished by differential operators.

New deformations for extended superspaces (N>1) are identified, with no N=1 analogues.

Abstract

Non commutative superspaces can be introduced as the Moyal-Weyl quantization of a Poisson bracket for classical superfields. Different deformations are studied corresponding to constant background fields in string theory. Supersymmetric and non supersymmetric deformations can be defined, depending on the differential operators used to define the Poisson bracket. Some examples of deformed, 4 dimensional lagrangians are given. For extended superspace (N>1), some new deformations can be defined, with no analogue in the N=1 case.